![]() I was fortunate to be in an honors class, with an excellent instructor who showed us some really interesting things (like the theorems of Ceva and Menelaus), but most students at my school had no such advantage. Another defect of the standard courses in geometry was that, because of the need to gently teach how to find and write proofs (in that rigid format), very little interesting geometry was taught the class was mostly proving trivialities. For example, Theorem 1 was word-for-word identical with Postulate 19 Theorem 1 was given a proof that didn't involve Postulate 19, so, in effect, we were shown that Postulate 19 is redundant, but the redundancy was never mentioned, and I still don't know why a redundant postulate was included in the first place. The textbook that we used also had some defects concerning proofs. They also got the idea that proofs are only for geometry subsequent courses (in the regular curriculum, not honors courses) didn't involve proofs. So I fear that many students got an inaccurate idea of what proofs are really like. These proofs, however, were in a very rigid format, with statements on the left side of the page and a reason for every statement on the right side. When I was in high school (in the early 1960's), Euclidean geometry was the only course in the standard curriculum that required us to write proofs. However, I am genuinely interested in hearing arguments both pro and con. Some related questions: is it necessary for high-school students to be exposed to proofs? If so, is there a more efficient mathematical subject in comparison to EG, for high school students, in order to learn what is a theorem, an axiom and a proof?įull disclosure: currently I am leading a campaign for the return of EG to the syllabus of the high schools of my country (Cyprus). I am interested in hearing arguments both for and against the return of EG to high school curricula. I teach in a University (not a high school), and we keep introducing new introductory courses, for math majors, as our new students do not know what a proof is. Thus EG came back, but not in its original form. ![]() About ten years later, there were general calls that geometry return, as the introduction of the alternative mathematical areas did not produce the desired results. (An exception is Russia!) And together with EG there was a gradual disappearance of mathematical proofs from the high school syllabus, in most European countries the trouble being (as I understand it) that most of the proofs and notions of modern mathematical areas which replaced EG either required maturity or were not sufficiently interesting to students, and gradually most of such proofs were abandoned. Analogous demotion/abolition of EG took place in most European countries during the 70s and 80s, especially in the Western European ones. Not totally abolished though: it is still a part of the syllabus, but without the difficult and interesting proofs and the axiomatic foundation. These ideas were influential, and Euclidean Geometry was gradually demoted in French secondary school education. ![]() In brief, the suggestion was to replace Euclidean Geometry (EG) in the secondary school curriculum with more modern mathematical areas, as for example Set Theory, Abstract Algebra and (soft) Analysis. See Dieudonné's address at the Royaumont seminar for his own articulated stance. 157), often associated in the popular mind with Bourbaki's general stance on rigorous, formalized mathematics (eschewing pictorial representations, etc.). ![]() Apparently Euclid died about 2,300 years ago (actually 2,288 to be more precise), but the title of the question refers to the rallying cry of Dieudonné, "A bas Euclide! Mort aux triangles!" (see King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts, p.
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